00:01
Okay, we are told that 49 % on average of van and pelons are repeat offenders.
00:08
So that means then p of being a repeat offender, so repeat is 0 .49.
00:19
It's changed from percent to decimal, which means then p of a non -repellen is 1 minus that, 0 .5.
00:34
It's a binomial problem.
00:37
And we can see here that success is 0 .49.
00:42
Wrong word ready to use there.
00:45
And failure is the 0 .51.
00:49
Okay, the first question says exactly 18 from 35 are repeat and i'll repeat offenders.
00:57
So, p of exactly 18.
01:05
So is the long way.
01:08
Of doing it first then i'll show you a shortcut exactly 18 is 0 .49 for repeat offenders i want 18 of them so power on 18 that implies that what i want is 17 non -repeat offenders you have 35 in total 18 repeat means 17 don't repeat the 18 plus 17 is 35 now number of of doing that the binomial number is 35 18 and what that means is 35 factorial over 17 factorial 18 factorial that's the ncr formula actually but that you can work out on a calculator or do the following it easier it will also equal on the ti 84 plus calculator is a function called binomial or binompedf and that you will find by pressing second the blue button followed by vars v -a -r -s on the right just below the arrow keys that brings up the menu for distributions you can't see it yet but go down with the arrow key pass number nine at the bottom until you reach item a by non -pd -f press enter and it says trials trials is number of people you've leading with here which is 35 the p value chance of success or success here is defined as being a repeat offender so that's 0 .49 the x value is i want to have 18 repeat offenders so 18 goes here we type that in 35 .49 and 18 repeat offenders paste and we get the answer 0 .128 what they want here.
03:22
Let's have a look.
03:27
Okay, no mention of accuracy.
03:30
So it's 0 .125, so let me say 0 .128, i should be fine.
03:37
If you work out this here, you get the exact same thing.
03:45
Okay, now in part b, what we have is p of at most 16, of most 16 repeat offenders.
04:01
So that means p of 0 1 2 3 up to 16 offenders at most 16 means 16 or below.
04:15
Now this i work out also the ti 84 plus calculator at this time functions called binom cdf not pdf cdf c for cumulative is it adds up each one.
04:29
You could work out binom pdf for 16, 15, 14, 13 down to zero and add it all up.
04:37
That's kind of crazy.
04:39
So binom cdf is it for you.
04:42
And all you do second vars again like before, go down.
04:49
This time pass number 9, pass binom pdf to item b, binom cdf.
04:57
Same input.
04:58
Trials 35 felons the p value is again 0 .49 and the x value is the number the highest one here it goes down from 16 to 0 always inclusive so type that in 35 .49 and 16 paste enter enter again 0 .416 so 414 to 3 decimal places.
05:37
And that is that one.
05:40
Okay, next we have p of at least 15 are repeat offenders.
05:47
So, p of at least 15 means p of 15, 16, up to, or 35 being repeat offenders.
06:03
Now here you have to work backwards because binom cdf does a number down to zero.
06:12
So what this will be is 1, a certain event, minus p of what i don't want, which would be 0, 1, 2, 3, up to 14.
06:27
So 15 to 35, the same as 1 minus 0 to 14...